Some crystal materials can perform well as optical materials, particularly for transmitting shorter wavelengths of light such as ultraviolet or deep ultraviolet light where most amorphous optical materials are less transmissive or more susceptible to optical damage. However, the ordered structure of crystalline optical materials in the form of repeating cells of atoms or molecules arranged in lattice can have directionally dependent properties unlike amorphous materials like glass. For example, refractive index can be affected by the direction at which light encounters periodic crystal structures. Such directionally dependent refractive index properties are referred to as birefringence.
Uniaxial crystal materials, such as calcium fluoride, which express three-dimensional symmetry on a unit cell scale, exhibit little birefringence except at shorter wavelengths in the deep ultraviolet spectrum where sub-unit asymmetries are apparent on a finer scale. Such birefringence, to the extent the birefringence remains consistent throughout the crystal structures, can be accommodated or even exploited by optical designs.
In actual crystals, defects interrupt the periodic order of crystal structures, which can degrade the performance of crystal optical materials. A major defect that affects the long-range cell order is a grain boundary. This is the junction or intersection of two crystals of the same material that have different orientations. The discontinuity in crystal structure is apparent when crossing a grain boundary and is generally not tolerable in precision optical materials. Such grain boundaries can be plentiful or rare depending on the crystal's content or history.
Another recurring defect in crystal structure is a subgrain boundary. As the name implies, these boundaries form inside individual crystal grains. Subgrain boundaries generally comprise groupings of dislocations or line defects in the material. Dislocations can be thought of as imperfect packing of the crystal unit cells. In the region immediately surrounding the dislocation, the dislocation causes disorder in the crystal structure but does not generally affect the material order further away from the dislocation site.
Dislocations can move through a grain of a crystal as the crystal material is stressed. Dislocations that group together into a network form the subgrain boundaries. These networks are energetically favorable to form because they decrease the energy associated with disorder from each individual dislocation. When crossing a subgrain boundary, a very slight orientation change occurs, which is much smaller than when crossing a grain boundary. The material on either side of a subgrain boundary will have almost the same orientation.
When subgrains are apparent throughout a crystal material, the crystal material is described as having a mosaic structure, made up by many smaller individual tiles (i.e., subgrains) that are all slightly misaligned relative to each other. In optical materials, high levels of mosaic are undesirable and thought to shorten the lifetime (e.g., service life) of crystal optical materials, particularly with respect to the transmission of shorter wavelengths in the deep ultraviolet spectrum.
Several methods are known for assessing the mosaic layout of crystal materials. However, each has drawbacks associated with measurement time, measurement equipment, material damage, or a lack of quantifiable results.
Since mosaic is disorder of the crystal lattice (i.e., relative misalignments within the periodic crystal structure), techniques that can determine lattice orientations are capable of detecting mosaic. X-ray probes are most widely used for determining relative orientations of the crystal lattice. For example, X-ray diffraction, soft X-rays, or X-ray topography are all capable of providing information on the mosaic level of a crystal.
X-ray diffraction uses a relatively low-powered, white source (low temporal coherence) X-ray beam to determine crystal lattice orientations. X-rays directed to the crystal surface constructively interfere with the crystal structure when the X-ray energy and lattice spacings and angles meet specific criteria. For example, constructive interference occurs at particular diffraction angles (referred to as Bragg diffraction) when the optical path-length difference between rays scattered from adjacent lattice planes equal an integral number of wavelengths. By collecting and analyzing the diffracted X-rays, the orientation of the crystal structure can be determined. In addition, by determining the crystal lattice orientations at several different locations in the crystal sample, an indication of the amount of mosaic present in the crystal sample can be estimated. However, such multiple exposures can take hours to complete per sample, and the X-rays expose the crystal to ionizing radiation that can damage the crystal material of the sample.
Soft X-rays are a much faster method of measuring mosaic. A much higher intensity X-ray beam passes directly though the crystal. Similar to X-ray diffraction, when certain conditions are met in the structure, some of the beam is deflected. By capturing this deflected beam and determining its width, a measure of mosaic can be estimated. The width of the deflected beam is affected by the amount of disorder in the crystal sample, and the beam is narrowest when the mosaic level is lowest. Scanning the soft X-ray beam allows for spatial information to be collected throughout the crystal sample. However, specialized equipment is required to carry out this method, which is available in only a few locations in the world. In addition, the X-rays expose the crystal sample to damaging ionizing radiation.
X-ray topography is another X-ray technique that can estimate the mosaic level. A high intensity X-ray beam (from a synchrotron) is highly collimated by passing the beam through slits that can be 100 meters apart. The highly collimated beam is directed to the crystal sample and a diffraction spot is collected. The crystal sample is translated through the beam to map reflections from its surface. Because the beam is so collimated, the diffraction spot can then be enlarged to see an image of how the crystal structure of the crystal surface varies. Again, highly specialized equipment is needed, and the exposure of the crystal sample to ionizing radiation can cause damage.
Besides the X-ray techniques for mosaic identification, several other methods have been used to estimate the amount of mosaic in crystal samples. The simplest involves cleaving the crystal sample and visually inspecting its surface. Since subgrains cause only slight changes in the crystal orientation, the material can be cleaved. Inspection of the cleaved surface of a crystal with high mosaic reveals a large number of subregions that are all slightly misaligned. However, the inspection is limited to the cleaved surface of the sample, the cleaving itself causes obvious damage, and the estimate of mosaic is highly subjective. At best a relative rating of low, medium, or high can be given.
Another method commonly used is to inspect crystal mosaic uses a cross polarizer to see the effects of stress on the crystal sample. Stress causes birefringence, and a cross polarizer shows areas with higher levels of stress as different colors. Mosaic, since it is disorder of the lattice, makes this color shift less uniform. Mosaic images from the cross polarizer appear as cobweb structures or as clouds. The method allows a quick mosaic evaluation, but is highly subjective and can only yield relative ratings of low, medium, and high. Even these ratings can be questionable, since the amount of birefringence seen is affected by both the crystal orientation and the tested sample length. A sample material with very low stress has low amounts of stress birefringence and therefore a low signal output, which makes estimates of mosaic more difficult.
Two other methods for observing mosaic effects involve using a shadowgraph technique or an optical homogeneity measurement. Because of disorder in the crystal sample, light passing through the sample can be slightly deflected. This can be seen using a high-powered light source projected through the crystal sample onto a special screen. Quantification, however, is problematic. Optical homogeneity of a sample crystal can also be measured as an indication of mosaic. However, the method tends to be labor intensive and quite slow.